Collective modes of the massless dirac plasma

We develop a theory for the long-wavelength plasma oscillation of a collection of charged massless Dirac particles in a solid, as occurring, for example, in doped graphene layers, interacting via the long-range Coulomb interaction. We find that the long-wavelength plasmon frequency in such a doped massless Dirac plasma is explicitly nonclassical in all dimensions with the plasma frequency being proportional to 1/sqrt[variant Planck's over 2pi]. We also show that the long-wavelength plasma frequency of the D-dimensional superlattice made from such a plasma does not agree with the corresponding D + 1-dimensional bulk plasmon frequency. We compare and contrast such Dirac plasmons with the well-studied regular palsmons in metals and doped semiconductors which manifest the usual classical long-wavelength plasma oscillation.